What is the derivative of 1/((x^2+a^2)^{n-1)} ?

The derivative of 1/((x^2+a^2)^{n-1)} is (x^2+a^2)^{-n}(-n+1)*2x

What is the first derivative of 1/((x^2+a^2)^{n-1)} ?

The first derivative of 1/((x^2+a^2)^{n-1)} is (x^2+a^2)^{-n}(-n+1)*2x

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative

(x^{2} + a^{2})^{- n} (- n + 1) \cdot 2 x

Solution steps

\frac{d}{d x} (\frac{1}{( x ^{2} + a ^{2} ) ^{n - 1}})

Treat

n, a

as a constant

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= \frac{d}{d x} ((x^{2} + a^{2})^{- n + 1})

Apply the chain rule:

(x^{2} + a^{2})^{- n} (- n + 1) \frac{d}{d x} (x^{2} + a^{2})

= (x^{2} + a^{2})^{- n} (- n + 1) \frac{d}{d x} (x^{2} + a^{2})

\frac{d}{d x} (x^{2} + a^{2}) = 2 x

= (x^{2} + a^{2})^{- n} (- n + 1) \cdot 2 x

What is the derivative of 1/((x^2+a^2)^{n-1)} ?
The derivative of 1/((x^2+a^2)^{n-1)} is (x^2+a^2)^{-n}(-n+1)*2x
What is the first derivative of 1/((x^2+a^2)^{n-1)} ?
The first derivative of 1/((x^2+a^2)^{n-1)} is (x^2+a^2)^{-n}(-n+1)*2x